PROFINITE COMPLETION OF GRIGORCHUK'S GROUP IS NOT FINITELY PRESENTED

Benli M. G.

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, vol.22, no.5, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 5
  • Publication Date: 2012
  • Doi Number: 10.1142/s0218196712500452
  • Journal Name: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Grigorchuk group, profinite completion, BRANCH GROUPS, PRESENTATIONS
  • Middle East Technical University Affiliated: No

Abstract

In this paper we prove that the profinite completion (G) over cap of the Grigorchuk group G is not finitely presented as a profinite group. We obtain this result by showing that H-2((G) over cap, F-2) is infinite dimensional. Also several results are proven about the finite quotients G/St(G)(n) including minimal presentations and Schur Multipliers.